6 papers
A Busemann hybrid projection-proximal point algorithm for optimization problems on Hadamard manifolds
R. Díaz Millán, O. P. Ferreira, M. S. Louzeiro +1
We study optimization problems on Hadamard manifolds, motivated by recent advances in geometric approaches to optimization on curved spaces, particularly those involving the struct…
Frank-Wolfe algorithm for star-convex functions
R. Diaz Millan, Orizon Pereira Ferreira, Julien Ugon
We study the Frank-Wolfe algorithm for minimizing a differentiable function with Lipschitz continuous gradient over a compact convex set. To extend classical complexity bounds to c…
Global minimisation of nonconvex functions by generalising the mirror descent method
Reinier Díaz Millán, Julien Ugon
In this paper we introduce two conceptual algorithms for minimising abstract convex functions. Both algorithms rely on solving a proximal-type subproblem with an abstract Bregman d…
Extragradient method with feasible inexact projection to variational inequality problem
R. Díaz Millán, O. P. Ferreira, J. Ugon
The variational inequality problem in finite-dimensional Euclidean space is addressed in this paper, and two inexact variants of the extragradient method are proposed to solve it.…
Frank--Wolfe algorithms for piecewise star-convex functions with a nonsmooth difference-of-convex structure
R. Díaz Millán, O. P. Ferreira, J. Ugon
In the present paper, we formulate two versions of Frank--Wolfe algorithm or conditional gradient method to solve the DC optimization problem with an adaptive step size. The DC obj…
Approximate Douglas-Rachford algorithm for two-sets convex feasibility problems
R. Díaz Millán, O. P. Ferreira, J. Ugon
In this paper, we propose a new algorithm combining the Douglas-Rachford (DR) algorithm and the Frank-Wolfe algorithm, also known as the conditional gradient (CondG) method, for so…